一般时间区间L~p-半鞅序列的单调极限定理
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摘要
基于倒向随机微分方程(BSDE)和非线性期望理论中惩罚方法的启发,研究并得到了一般时间区间上L~p-半狹序列的单调极限定理.该结果的证明并非经典结果的平凡推广,新的框架让我们面对许多新问题,它将在一般框架下g-上鞅的Doob-Meyer型分解以及受限BSDE解的存在性等问题的探索中发挥重要作用.
In this paper, a new version of monotonic limit theorem is established for a sequence of L~p-semimartingales on general time interval, motivated by the penalization method in the theories of backward stochastic differential equations(BSDEs for short) and nonlinear expectations. It is just the general framework that makes us have to tackle many new problems. And also this non-trivial result plays a key role in exploring the more general form of nonlinear Doob-Meyer Decomposition of g-supermartingale and the existence of solutions to BSDEs with constraints.
In this paper, a new version of monotonic limit theorem is established for a sequence of L~p-semimartingales on general time interval, motivated by the penalization method in the theories of backward stochastic differential equations(BSDEs for short) and nonlinear expectations. It is just the general framework that makes us have to tackle many new problems. And also this non-trivial result plays a key role in exploring the more general form of nonlinear Doob-Meyer Decomposition of g-supermartingale and the existence of solutions to BSDEs with constraints.
引文
[1] Pardoux E,Peng S. Adapted solution of a backward stochastic differential equation[J]. Systems&Control Letters, 1990, 14(1):55-61.
[2] El Karoui N, Kapoudjian C, Pardoux E, et al. Reflected solutions of backward SDE's, and related obstacle problems for PDE's[J]. The Annals of Probability, 1997,25(2):702-737.
[3] Cvitanic J, Karatzas I. Backward stochastic differential equations with reflection and Dynkin games[J]. The Annals of Probability, 1996, 24(4):2024-2056.
[4] Peng S. Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type[J]. Probability Theory and Related Fields, 1999, 113(4):473-499.
[5] Peng S, Xu M. The smallest g-supermartingale and reflected BSDE with single and double L2 obstacles[J]. Ann. Inst. H. Poincare Probab. Statist, 2005, 41(3):605-630.
[6] Dunford N J, Schwartz J T. Linear operators:V. 1:general theory[M]. New York:Interscience Publishers, Inc, 1988.
[7] Bayraktar E, Yao S. Doubly reflected BSDEs with integrable parameters and related Dynkin games[J]. Stochastic Processes and Their Applications, 2015, 125(12):4489-4542.
[2] El Karoui N, Kapoudjian C, Pardoux E, et al. Reflected solutions of backward SDE's, and related obstacle problems for PDE's[J]. The Annals of Probability, 1997,25(2):702-737.
[3] Cvitanic J, Karatzas I. Backward stochastic differential equations with reflection and Dynkin games[J]. The Annals of Probability, 1996, 24(4):2024-2056.
[4] Peng S. Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type[J]. Probability Theory and Related Fields, 1999, 113(4):473-499.
[5] Peng S, Xu M. The smallest g-supermartingale and reflected BSDE with single and double L2 obstacles[J]. Ann. Inst. H. Poincare Probab. Statist, 2005, 41(3):605-630.
[6] Dunford N J, Schwartz J T. Linear operators:V. 1:general theory[M]. New York:Interscience Publishers, Inc, 1988.
[7] Bayraktar E, Yao S. Doubly reflected BSDEs with integrable parameters and related Dynkin games[J]. Stochastic Processes and Their Applications, 2015, 125(12):4489-4542.